Such devices confine hot, electrically charged gas - or plasma - in powerful magnetic fields. But heat inevitably flows through the system and becomes separated, or scraped off, from the edge of the plasma and flows into an area called the divertor chamber.

The challenge is to prevent a thin and highly concentrated layer of heat from reaching and damaging the plate that sits at the bottom of the divertor chamber and absorbs the scrape-off flow. Such damage would halt fusion reactions, which take place when the atomic nuclei, or ions, inside the plasma merge and release energy.

Solving this problem will be vital for future machines like ITER, the world’s most powerful tokamak, which the European Union, the United States, and five other countries are building in France to demonstrate fusion as a source of clean and abundant energy. The project is designed to produce 500 megawatts of fusion power in 400 second-long pulses, which will require researchers to spread the scrape-off heat as much as possible to protect the divertor plate. Goldston’s model could help guide such efforts.

The way plasma flows inside tokamaks provided the major clue. The ions within the charged gas gyrate swiftly along the magnetic field lines while drifting slowly across the lines. At the same time, the electrons also in the plasma travel very rapidly along the lines and carry away most of the heat. Goldston arrived at his prediction by determining how fast these subatomic particles flow into the divertor region, and how long it therefore takes them to reach it. The result “is what we call a ‘heuristic’ estimate, based on the key aspects of the physics, but not a detailed calculation,” said Goldston.

His estimate confirmed that the width of the scrape-off layer nearly matched the results of a calculation, made without considering turbulence, for determining how far the ions drift away from their field lines. “What’s stunning is how closely the values correspond to the data, both in absolute value and in variation with the plasma current, magnetic field, machine size and input power,” Goldston said. “This does not mean that turbulence plays no role, but it suggests that for the highest performance conditions, where turbulence is weakest, the motion of the ions is dominated by non-turbulent drift effects.” This will be true in the case of ITER, he added, since it is designed to operate in high-performance conditions.

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